Remaining useful life (RUL) estimation plays a vital role in the prognostics and health management of degrading systems. For complicated degrading systems, the associated degradation processes are not only subjected to the nonlinearity in the degradation evolving paths but are also influenced by three important sources of variability, i.e., temporal variability, unit-to-unit variability, and measurement variability. However, current studies do not consider the above key factors jointly. Toward this end, this paper presents a general nonlinear degradation model to characterize the degradation nonlinearity and the three-source variability simultaneously. By constructing a state-space model and applying the Kalman filtering technique, we present the method of the RUL estimate with three-source variability and derive the analytical form of the probability density function of the RUL with three-source variability and the degradation nonlinearity approximately, which can be real-time updated with the available observations. As such, the effects of the degradation nonlinearity and three-source variability are propagated into the RUL estimate. In addition, the unknown parameters of the presented nonlinear model are estimated using the maximum likelihood estimation approach. For demonstrating the presented approach, comparative studies are conducted. The results verify that the proposed approach improves the model fitting and the accuracy of the RUL estimate.